This study is limited to patients with classic congenital adrenal hyperplasia due to 21-hydroxylase deficiency, but has the potential to significantly improve the lives of patients with other forms of adrenal insufficiency. Each of these diseases requires life-long treatment and this novel approach to drug delivery has the potential to significantly improve patients lives. This pilot study is fully enrolled and is in follow-up only status and data analysis is underway. In addition, this study will provide information on the safety and tolerability of using a pump to deliver hydrocortisone, and will generate data that will be used in the design of future studies.